Local rigidity of holomorphic curves in the complex Grassmann manifold G(2,6)

Jie Fei; Xiaowei Xu

doi:10.1016/j.geomphys.2017.08.002

Local rigidity of holomorphic curves in the complex Grassmann manifold G(2,6)

Jie Fei, Xiaowei Xu^*

^*Corresponding author for this work

Department of Pure Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper, we first obtain the Gauss equation for the non-degenerate holomorphic immersions from a Riemann surface into the complex Grassmann manifold G(2,6). By using it, we prove that any two linearly full non-degenerate holomorphic curves in G(2,6) are congruent if they have the same first and second fundamental forms.

Original language	English
Pages (from-to)	438-451
Number of pages	14
Journal	Journal of Geometry and Physics
Volume	121
DOIs	https://doi.org/10.1016/j.geomphys.2017.08.002
Publication status	Published - Nov 2017

Keywords

Complex Grassmann manifold
Gauss equation
Holomorphic curves
Pseudo-holomorphic sequence

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10.1016/j.geomphys.2017.08.002

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title = "Local rigidity of holomorphic curves in the complex Grassmann manifold G(2,6)",

abstract = "In this paper, we first obtain the Gauss equation for the non-degenerate holomorphic immersions from a Riemann surface into the complex Grassmann manifold G(2,6). By using it, we prove that any two linearly full non-degenerate holomorphic curves in G(2,6) are congruent if they have the same first and second fundamental forms.",

keywords = "Complex Grassmann manifold, Gauss equation, Holomorphic curves, Pseudo-holomorphic sequence",

author = "Jie Fei and Xiaowei Xu",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

month = nov,

doi = "10.1016/j.geomphys.2017.08.002",

language = "English",

volume = "121",

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T1 - Local rigidity of holomorphic curves in the complex Grassmann manifold G(2,6)

AU - Fei, Jie

AU - Xu, Xiaowei

PY - 2017/11

Y1 - 2017/11

N2 - In this paper, we first obtain the Gauss equation for the non-degenerate holomorphic immersions from a Riemann surface into the complex Grassmann manifold G(2,6). By using it, we prove that any two linearly full non-degenerate holomorphic curves in G(2,6) are congruent if they have the same first and second fundamental forms.

AB - In this paper, we first obtain the Gauss equation for the non-degenerate holomorphic immersions from a Riemann surface into the complex Grassmann manifold G(2,6). By using it, we prove that any two linearly full non-degenerate holomorphic curves in G(2,6) are congruent if they have the same first and second fundamental forms.

KW - Complex Grassmann manifold

KW - Gauss equation

KW - Holomorphic curves

KW - Pseudo-holomorphic sequence

UR - http://www.scopus.com/inward/record.url?scp=85030858342&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2017.08.002

DO - 10.1016/j.geomphys.2017.08.002

M3 - Article

AN - SCOPUS:85030858342

SN - 0393-0440

VL - 121

SP - 438

EP - 451

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

Local rigidity of holomorphic curves in the complex Grassmann manifold G(2,6)

Abstract

Keywords

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